Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4582547 | Expositiones Mathematicae | 2007 | 15 Pages |
Abstract
In this expository note, we give a simple conceptual proof of the Hirzebruch proportionality principle for Pontrjagin numbers of non-positively curved locally symmetric spaces. We also establish (non)-vanishing results for Stiefel–Whitney and Pontrjagin numbers of (finite covers of) the Gromov–Thurston examples of compact negatively curved manifolds. A byproduct of our argument gives a constructive proof of a well-known result of Rohlin: every closed orientable 3-manifold bounds orientably. We mention some geometric corollaries: a lower bound for degrees of covers having tangential maps to the non-negatively curved duals and estimates for the complexity of some representations of certain uniform lattices.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jean-François Lafont, Ranja Roy,